Searching for string in regular expression

I am working on Protein and DNA sequences. When you have a protein sequence it can be translated in to DNA sequence in many ways. A nice way to express this is using regular expression. I would like to create this long regular expression for a protein sequence, and than seach for a smaller string. So that is the other way around of what regular expression does. Is there a way to do this?

I see a way, but there is some work to do. First you convert your regular expression to a NFA (non deterministic finite automaton) with a start state and
an accept state. In this NFA, you add an epsilon-transition from the start state to every other state and an epsilon transition from any state to the accept state.
This NFA should be able to find your subsequences.

A second step could be to convert the NFA into a deterministic automaton (DFA) to produce a fast tool. You could use a program like this one for the conversion (again there is some work, because the NFA in this link doesn't seem to have epsilon transitions).

If you have only not optional alternatives without repeats in [], you could do something like this to avoid complicated transformations (you could improve the matching with more advanced string matching algorithm) :